Math = Love: February 2013

Thursday, February 14, 2013

Valentine's Day

Today is Valentine's Day.  I told my students that I had wanted to get them each a Valentine.  But, I went to Wal-Mart, and they didn't have any mathematical valentines.  So, I handed each of my students a strip of colored paper.  I told them that I still got them a Valentine; there was just some assembly required.

Without telling them what we were doing, I instructed them to cut their strip of paper in half.  We folded each strip into a mobius strip, one twisted to the right and one twisted to the left.  Then, we glued the two mobius strips together so they were perpendicular to one another.  Right when my students were really starting to wonder what we were making, I forced them to set their mobius strips aside to let the glue dry.  I really enjoyed getting to introduce my students to the concept of a mobius strip.  Only one student had heard of a mobius strip before.  And, she only remembered it from Vi Hart's Hexaflexagon video.

My Algebra 1 students spent the class period reviewing how to graph absolute value equations, finding slope from a table, and measures of central tendency.  Then, we started looking at more word problems together as a class.  I chose EOI practice problems that required more critical thinking skills than particular Algebra 1 skills.  I am trying to expose my students to as many different problem types as possible before the EOI in April.

Of course, my students did not want to do any math today.  They tried every sort of way possible to convince me that there was no reason to do school work on Valentine's Day.  Once we got started with the word problems, I think they actually enjoyed themselves.  We had some great discussions while trying to match scenarios with graphs.  I think I'm going to try to find some time to fit Dan Meyer's Graphing Stories into my curriculum.  

During the last five minutes of class, we finished our mystery valentines.  I instructed the students to cut both of their mobius strips in half.  The students were hesitant to do so.  They were convinced if they cut through the sections that had been glued that it would fall apart.  I assured them that I knew what I was doing.  And, in the end, they were pleasantly surprised to find two interlocking hearts.  It was a lot of fun doing this short activity with my students.  Plus, mobius strips are mathematical.  And, we discussed mathematical terms such as "perpendicular."

Inter-locking Mobius Strip Hearts.
This one isn't the prettiest, but it was the only one that was left behind in my classroom.
Instructions here:   
I really love my job.

Wednesday, February 13, 2013

Absolute Value Foldables and a 3-Hole Punch Story

[If you're not interested in absolute value, there is a pretty funny story about a 3-hole punch at the very end.  Or, maybe it's not funny.  Maybe it's sad.  Either way, it was a memorable experience.]

This week, I started introducing the concept of absolute value to my Algebra 1 students.  Our Algebra 1 textbooks introduce the concept of absolute value in Algebra 1.  It introduces graphing absolute value equations in the same chapter where graphing linear equations is taught.  Of course, I don't use the textbooks.  I keep one by my desk as a reference, but the rest of the books are collecting dust on my shelves.

This summer, I had planned to introduce absolute value using the textbook sequence.  I even created some pages for my students' interactive notebooks.

I never used this page, though.  Actually, I decided it was in the best interest of my students to postpone discussing absolute value until later in the school year.  When I started working with my students at the beginning of the year, I realized just how low many of them were.  There were a lot of middle school math topics that I had to reteach.  So, I made the decision to take certain concepts and postpone them until later in the school year.  I was hoping that if I refined my focus I could build up my students' math levels and make them more confident.  Then, with more confidence, we could start looking at concepts such as fractions, absolute value, probability, etc.

So, Monday was my students' first experience with absolute value in Algebra 1.  A few students who took Algebra last year knew what absolute value was.  A few others wrongly described absolute value as meaning the opposite.  They thought it meant that you just changed the sign.

My students had been working really hard at multiplying binomials and factoring quadratics for the past two weeks.  Test scores were not exactly where I had wanted them, but at the same time I was proud of my students because I have seen them grown an incredible amount since meeting them in August.  In August, I would not have thought that my students would be factoring quadratics with a leading term greater than one.  But, we've gotten here.  We still need some more practice with factoring, but we will continue reviewing it and practicing it for the remainder of the semester.  And, it was a Monday.  So, I decided to kinda ease into our absolute value unit using the Estimating Age activity from Dan Meyer's Algebra Curriculum (Week 3.)

Estimating Ages Chart
I picked 15 of the celebrities from his file.  I used their birthdays to calculate their current age.  I typed up a half-sheet of paper for students to record their guesses.  It's not perfect.  After using it once, I realized that I should have added a fourth column for students to record the difference between the actual age and their guess.  I don't know if it would be of use to anyone, but I have uploaded my file below.

We went through each celebrity.  As a class, the students tried to guess who the celebrity was.  This led to some very enlightening conversations.  My students didn't know who Natalie Portman was.  They didn't recognize Penelope Cruz.  I thought for sure that the would recognize Julia Roberts.  No, they thought she was a character off of Sex and the City.  We had arguments over whether Tobey Maguire's real name was Tobey Maguire or Peter Parker.  I was shocked to learn that one of my students thought Judi Dench was James Bond's mother.  But, my other classes didn't even know that she had played M in the James Bond movies.  Somehow, Ronald Reagan got brought up in my 8th grade Algebra class, and I learned that two of my 8th graders had no clue who Ronald Reagan was.  One student told me that they thought Morgan Freeman looked like the president of Africa.  But, others tried to convince me that Morgan Freeman looked the exact same as Samuel Jackson and Denzel Washington.  Another student was convinced that Will Smith was only 21.  

After my students had recorded their guesses for the age of each celebrity, I revealed the correct ages.  They  wrote down in the margin how far off they were.  Then, we totaled this column.  The student with the lowest total won.  And, I didn't realize how much of a controversy my award would cause.  Up for grabs was a much-coveted "Super Student Award."  I picked these up at Dollar General during a 75% off school supplies clearance sale.  So, I picked up a few packs of awards.  At 25 cents for 24 awards, it was too good of a deal to pass up.  I thought my students might consider them childish, but I was wrong...  

Super Student Award
One student was so mad when he didn't win the award that he crumpled up his paper, tossed it across the room, and pouted for the rest of the class period.  He tried every way he could to get me to just write him a certificate, too.  I told him that I couldn't do that; he would have to find a way to earn one.  Now, he asks every day if we are going to play the game again so he can win an award.

After playing the celebrity age guessing game, I started to transition to absolute value by asking my students to consider a scenario where a celebrity was actually 55.  If one person guessed 51 and another person guessed 59, who would win?  One of my classes was convinced that the person who guessed 51 would win because it just had to be like the Price is Right where you automatically lose if you guess too high of a number.  I assured them that we weren't following the rules of the Price is Right.  Finally, we agreed that it was a tie because both guesses were the same distance from the true celebrity age.

In math, we aren't worried about how close a number is to a celebrity's age.  Instead, we want to know how close a number is to zero on the number line.  We filled out a Frayer Model on absolute value to glue in our interactive notebooks.

Absolute Value Frayer Model
 We ended up Day 1 of the unit by practicing some order of operation problems that involved absolute value.  This was a great way to review absolute value without feeling like I was losing valuable class time.  A lot of my students left my class this day feeling more confident about math than I had seen them all semester. Our two previous units on exponent rules and polynomials have left some of my students with lower grades than last semester.  I hope my students realize that I am pushing them because I care for them.  We have made great strides this school year!

Day 1 of the Unit - Interactive Notebook Entry
On Day 2 of the unit, we started graphing absolute value equations.  I had my students do this using a t-chart.  I created a booklet foldable to guide our in-class practice time.  As a class, we graphed 5 absolute value equations together.  Then, I gave them 6 more to complete in-class on their own.

Graphing Absolute Value Equations Booklet Foldable - Outside

Graphing Absolute Value Equations Booklet Foldable - Inside
We had some great conversations while graphing these.  It was exciting to see them discover that absolute value equations form a "V" when graphed.  I intentionally had them graph y = |x| and see the shape for themselves before writing the definition of absolute value equations on the cover.  Initially, some students assumed that they must have did something wrong since the graph wasn't a straight line.

We talked a lot about why the y-values for some graphs could be negative.  Eventually they realized that it made a big difference whether the subtraction happened inside the absolute value bars or outside the absolute value bars.  I've been trying to incorporate more foldables into this semester.  Last semester, I did a ton of foldables.  I kind of stopped for a few weeks this semester.  I think it was a mixture of feeling uninspired / rushed.  I think all of my students love foldables, but they are really crucial to the success of my IEP students.  These students need examples to look out.  They need a reference to remind them what steps to take.

I think next time I teach this unit, I want to have my students write out more of the steps that you go through to take your input x to reach the output y.  Because this doesn't capture that process, it is not an amazing resource for my IEP students or students who were absent the day we went over this lesson.

Day 3 of our unit focused on graphing absolute value transformations.  In Oklahoma, Algebra 1 students are only tested on horizontal and vertical translations.  I used the same graphic organizer that I used with my Algebra 2 students at the beginning of the school year.  I'm more worried about my students realizing that changing the equation will shift the graph than making them memorize what aspect of the equation creates what shift.  That will come in Algebra 2.

Absolute Value Transformations
In one class, one of my students wanted to write "It went jogging" or "It went on a diet" to describe the transformation of number 5 above.  My students definitely know how to make me smile!  Life is definitely never dull around them.

To illustrate that last statement, I have a story to tell.  One of my students borrowed my three-hole punch today.  She was taking colored paper and using it to create dividers in her binder.  Instead of returning it to my desk when the bell rang, she left it on her desk.  The next hour, my 8th graders arrive and start working on their bellwork.  After completing our "Beat the School" problem, I hear one of my students saying "What in the world is that?"  When I look at him, he is frantically pointing at something in front of him.  I'm imagining all kinds of terrible creepy, crawly, or yucky things that could be causing this response.  No, he is pointing at the three-hole punch.  He's never seen one before in his life.  I thought he was exaggerating.  No, he was telling the truth.  I tried my best to explain the foreign concept of a three-hole punch.  Other students started confessing that they didn't know what it did either.  Finally, another student demonstrates the three-hole punch.

Instead of amazement, the questioning student responds with confusion.  Why would you need something to punch three holes into your paper?  Realizing that I can't assume anything, I asked the class if anyone else knew what a three-hole punch was.  3 hands.  Out of 9.  Two-thirds of my class has never used a three-hole punch.  Oh my goodness.  I attempted another explanation.  Do you know what a binder is?  It has three metal rings.  We use the three-hole punch to punch the holes in the paper so we can put it in the rings.  To this, I was told that it was really unnecessary.  Instead, my students thought that notebook paper was meant to go in the rings.  That's why notebook paper comes with the holes.  Any paper that doesn't come with the holes is meant to go in the pockets of the binder.  Some days I wonder what this world is coming to...      

Download files here.

Heart Smiles

Earlier this semester, I received a letter from a student that just made my heart smile.  It was a result of the Origami Letter Project.  I want to share this letter with you today.  When I organized this project, I was not seeking out letters for myself.  I was seeking out letters for others.  My students have always been really candid with me.  They tell me when they love my lessons.  And, they tell me when they don't.  I value their feedback.  Since I'm not in others' classrooms, I don't know if the students give them this feedback or not.  I hoped that they did, but I wanted to make sure that our teachers, administration, and support staff felt valued. 

Still, I'm thankful for those letters I received.  Some of them surprised me since they are from those students who aren't as vocal about their feelings and opinions.  And, I'm glad I gave them a chance to make someone's day in a way that was comfortable for them.    

One of my students wrote me this letter.

Ms. Hagan

Thank you so much for teaching me math.  You are the best math teacher ever.  I never learned math as easy as you teach us.  I have never had this good of a grade in math.  I hope I have you ever year till I graduate.  Thank you for everything.  

This is why I teach.  This is why I'm at school this week even though I don't feel 100%.  This is why I spend hours creating games and foldables and activities for my students.  My students need me.  I am making a difference in their lives.  And, they are making a difference in my life. 

Monday, February 11, 2013

Algebra 2 Describing Graphs Unit

Happy Monday!

I want to take this opportunity to thank everyone for all of the well-wishes and blog/twitter/pinterest love of late.  You guys have no idea how much you mean to me!

For Made 4 Math Monday, I want to share some resources I created for a recent Algebra 2 unit on describing graphs.

I introduced this unit to my Algebra 2 students by having them play graphing pictionary.  I used the domain and range graphing cards from Zero-Knowledge Proofs.  I gave each student two pages of cards to cut apart and keep in their notebook.  My students were surprisingly impressed by the small pocket we created to keep the cards in.  

Card Pocket for Interactive Notebook

Domain / Range Pictionary Cards

I had the students break up into pairs.  One student's job was to be the describer.  The other student was the drawer.  I gave students one minute to describe the graph to their partner.  It was quite enlightening to just walk around the room and listen to the vocabulary my students were using.  I was hoping to hear students discussing the domain, range, x-intercepts, or y-intercepts.  I hadn't introduced these terms yet, but I was hoping that they had been introduced to these concepts in Algebra 1.  I didn't hear any of these specific terms, but I did get extremely excited when I heard a student use the word "quadrant."    

(I really wish I had thought of letting my students play this again at the end of the unit to show how much they had grown!)

After letting the students struggle through the process, I attempted to refresh their memories of the concepts of domain and range.  

On day 2 of the unit, we created a foldable to summarize the three types of notation for domain/range.  You can read more about this foldable here.

Domain / Range Notation Foldable

After creating the foldable, we wrote the domain and range of the back of each of the graphs from our set of pictionary cards.  I intended for my students to be able to use these as flashcards, but I never saw them use them as such in class.

My next goal was for students to be able to recognize x-intercepts, y-intercepts, maximum and minimum values, and vertical and horizontal asymptotes.

I summarized these for my students in a booklet foldable for their interactive notebooks.
Characteristics of Graphs and Functions Foldable - Outside

Characteristics of Graphs and Functions Foldable - Inside
My students seemed to easily grasp the concepts of intercepts, maximums, and minimums.  The concept of an asymptote seemed to elude most of them.  I did use the HOY VUX mnemonic to help my students remember how to write the equations of horizontal and vertical lines.  But, I'm still not happy with my introduction of asymptotes.  I taught this unit before teaching rational expressions, so I couldn't exactly explain to my students what caused asymptotes.  This is definitely towards the top of my "figure out how to teach this better next year" list.  

Download file here

Sunday, February 10, 2013

It's been a while...

Well, despite all my efforts, my precautionary measures failed.

Teaching has definitely changed me.  I've never thought so much about germs or the simple act of touching a door knob. I now understand why my high school chemistry teacher had a cup of pencils that she allowed students to use and a cup of pencils that were only for her use.  I'm pretty sure that I've used more hand sanitizer in the past few weeks than the rest of my life combined.

Luckily, it's just a head cold instead of one of the more serious things going around.  Still, I'm tired of the sniffling and coughing and sneezing.  I taught Thursday and Friday with a sore throat, and I could definitely tell I wasn't at the top of my game as a result.

I had a surprise visitor in my classroom on Friday afternoon, though.  A student from a local university was in the building to observe one of our science teachers.  When the science teacher had to leave, the student was somehow directed to my classroom to observe.  I was happy to have her, but I felt kinda unprepared.  I didn't feel great.  My students were coming back after not doing so well on yesterday's test.  My desk was a disaster zone.  It's crazy to think that I was that college student a year ago.  And, now, I have college students observing me.        

I want to apologize for my absence in the math blogging/twitter world of late.  The first year of teaching, as I'm finding out, can be rather overwhelming.  School drama and responsibilities have left me exhausted.  I've learned a lot from the experiences, though, and I hope to find the time to share what I have been learning with you all,

I know this is long overdue.  But, I'm jumping back into the blogging world today with a graphic organizer template I created to introduce graphing inequalities to my Algebra 2 students.  Students filled this out and glued it in their interactive notebooks.  I posted a picture of this last semester, but I never posted the template.  Oops...

Enjoy the file!